There are many methods relating to interaction between immiscible fluids in a smoothed particle hydrodynamics (hereinafter, simply referred to as “SPH”) based fluid simulation. Particularly, there are two methods showing good visualization results in a graphics animation field: a first method using surface tension and a second method of changing velocities and positions of particles.
The first method uses property in which particles on a surface do not have a force maintaining balance with an inwardly acting force so that the particles on a surface are unstable than particles in the fluids and tend to form a sphere having the smallest surface. In this method, a force in proportion to magnitude of curvature acts in the normal direction of the particles. That is, the first method relates to a shape of a group of fluid particles.
However, in case of setting the surface tension to be weak in the first method, it is difficult to control mixing and scattering of the particles due to differences in velocities and pressures thereof occurring when the fluids collide. In case of setting the surface tension to be strong, the fluids shrink to overall form a sphere and stability of a system is damaged.
The second method of changing velocities and positions of particles detects collisions between the particles and changes the velocities and positions of the particles to prevent the particles from colliding with each other. This method shows a good result in simulating fluids which are not mingled with each other at all.
However, the collision detection as shown in FIG. 1A required to be performed in every simulation steps in the second method takes a considerably long calculation time. Further, in the second method, the collisions are prevented by instantly changing the calculated positions of the particles as shown in FIG. 1B to those as shown in FIG. 1C. However, distances between the particles are too short in FIG. 1C, which damages stability of a system in the next simulation step.